All Outputs (91)

Mathematical neuroscience: from neurons to networks (2015)
Book Chapter
Coombes, S. (2015). Mathematical neuroscience: from neurons to networks. In C. Dogbe (Ed.), Actes du colloque "EDP-Normandie" : Le Havre 2015. Fédération Normandie Mathématiques

The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this talk I will describe how to build tractable tissue level models that maintain a strong link with biophysical reality. T... Read More about Mathematical neuroscience: from neurons to networks.

Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes (2015)
Journal Article
Thul, R., Rietdorf, K., Bootman, M. D., & Coombes, S. (2015). Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes. Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, 1853(9), https://doi.org/10.1016/j.bbamcr.2015.02.019

Atrial myocytes in a number of species lack transverse tubules. As a consequence the intracellular calcium signals occurring during each heartbeat exhibit complex spatio-temporal dynamics. These calcium patterns arise from saltatory calcium waves tha... Read More about Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes.

Spots: breathing, drifting and scattering in a neural field model (2014)
Book Chapter
Coombes, S., Schmidt, H., & Avitabile, D. (2014). Spots: breathing, drifting and scattering in a neural field model. In S. Coombs, P. Beim Graben, R. Potthast, & J. Wright (Eds.), Neural fields: theory and applications (187-211). Springer. https://doi.org/10.1007/978-3-642-54593-1_7

Two dimensional neural field models with short range excitation and long range inhibition can exhibit localised solutions in the form of spots. Moreover, with the inclusion of a spike frequency adaptation current, these models can also support breath... Read More about Spots: breathing, drifting and scattering in a neural field model.

Travelling waves in models of neural tissue: from localised structures to periodic waves (2014)
Journal Article
Meijer, H., & Coombes, S. (2014). Travelling waves in models of neural tissue: from localised structures to periodic waves. EPJ Nonlinear Biomedical Physics, 2(3), https://doi.org/10.1140/epjnbp16

We consider travelling waves (fronts, pulses and periodics) in spatially extended one dimensional neural field models. We demonstrate for an excitatory field with linear adaptation that, in addition to an expected stable pulse solution, a stable anti... Read More about Travelling waves in models of neural tissue: from localised structures to periodic waves.

Travelling waves in a neural field model with refractoriness (2013)
Journal Article
Meijer, H. G., & Coombes, S. (2014). Travelling waves in a neural field model with refractoriness. Journal of Mathematical Biology, 68(5), 1249-1268. https://doi.org/10.1007/s00285-013-0670-x

At one level of abstraction neural tissue can be regarded as a medium for turning local synaptic activity into output signals that propagate over large distances via axons to generate further synaptic activity that can cause reverberant activity in n... Read More about Travelling waves in a neural field model with refractoriness.

A biophysical model of endocannabinoid-mediated short term depression in hippocampal inhibition (2013)
Journal Article
Zachariou, M., Alexander, S. P., Coombes, S., & Christodoulou, C. (2013). A biophysical model of endocannabinoid-mediated short term depression in hippocampal inhibition. PLoS ONE, 8(3), Article e58296. https://doi.org/10.1371/journal.pone.0058926

Memories are believed to be represented in the synaptic pathways of vastly interconnected networks of neurons. The
plasticity of synapses, that is, their strengthening and weakening depending on neuronal activity, is believed to be the basis
of lea... Read More about A biophysical model of endocannabinoid-mediated short term depression in hippocampal inhibition.

Limitations of perturbative techniques in the analysis of rhythms and oscillations (2013)
Journal Article
Lin, K. K., Wedgwood, K. C., Coombes, S., & Young, L.-S. (2013). Limitations of perturbative techniques in the analysis of rhythms and oscillations. Journal of Mathematical Biology, 66(1-2), https://doi.org/10.1007/s00285-012-0506-0

Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are “sufficiently weak”, an assumption that is not always valid when... Read More about Limitations of perturbative techniques in the analysis of rhythms and oscillations.

Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves (2012)
Journal Article
Thul, R., Coombes, S., & Bootman, M. D. (2012). Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves. Frontiers in Physiology, 3, Article 279. https://doi.org/10.3389/fphys.2012.00279

Clusters of ryanodine receptors within atrial myocytes are confined to spatially separated layers. In many species, these layers are not juxtaposed by invaginations of the plasma membrane (transverse tubules; 'T-tubules'), so that calcium-induced-cal... Read More about Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves.

Interface dynamics in planar neural field models (2012)
Journal Article
Coombes, S., Schmidt, H., & Bojak, I. (2012). Interface dynamics in planar neural field models. Journal of Mathematical Neuroscience, 2(1), 1-46. https://doi.org/10.1186/2190-8567-2-9

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patt... Read More about Interface dynamics in planar neural field models.

Using evolutionary algorithms for fitting high-dimensional models to neuronal data (2012)
Journal Article
Svensson, C.-M., Coombes, S., & Peirce, J. (2012). Using evolutionary algorithms for fitting high-dimensional models to neuronal data. Neuroinformatics, 10(2), https://doi.org/10.1007/s12021-012-9140-7

n the study of neurosciences, and of complex biological systems in general, there is frequently a need to fit mathematical models with large numbers of parameters to highly complex datasets. Here we consider algorithms of two different classes, gradi... Read More about Using evolutionary algorithms for fitting high-dimensional models to neuronal data.

Neuronal spike-train responses in the presence of threshold noise (2012)
Journal Article
Coombes, S., Thul, R., Laudanski, J., Palmer, A., & Sumner, C. (in press). Neuronal spike-train responses in the presence of threshold noise. Frontiers in Life Science, 5(3-4), https://doi.org/10.1080/21553769.2011.556016

The variability of neuronal firing has been an intense topic of study for many years. From a modelling perspective it has often been studied in conductance based spiking models with the use of additive or multiplicative noise terms to represent chan... Read More about Neuronal spike-train responses in the presence of threshold noise.

Subcellular calcium dynamics in a whole-cell model of an atrial myocyte (2012)
Journal Article
Thul, R., Coombes, S., Roderick, H. L., & Bootman, M. D. (2012). Subcellular calcium dynamics in a whole-cell model of an atrial myocyte. Proceedings of the National Academy of Sciences, 109(6), 2150-2155. https://doi.org/10.1073/pnas.1115855109

In this study, we present an innovative mathematical modeling approach that allows detailed characterization of Ca 2+ movement within the three-dimensional volume of an atrial myocyte. Essential aspects of the model are the geometrically realistic re... Read More about Subcellular calcium dynamics in a whole-cell model of an atrial myocyte.

Nonsmooth dynamics in spiking neuron models (2011)
Journal Article
Coombes, S., Thul, R., & Wedgwood, K. C. (2012). Nonsmooth dynamics in spiking neuron models. Physica D: Nonlinear Phenomena, 241(22), https://doi.org/10.1016/j.physd.2011.05.012

Large scale studies of spiking neural networks are a key part of modern approaches to understanding the dynamics of biological neural tissue. One approach in computational neuroscience has been to consider the detailed electrophysiological propertie... Read More about Nonsmooth dynamics in spiking neuron models.

Atrial cardiomyocyte calcium signalling (2011)
Journal Article
Bootman, M. D., Smyrnias, I., Thul, R., Coombes, S., & Roderick, H. L. (2011). Atrial cardiomyocyte calcium signalling. Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, 1813(5), 922-934. https://doi.org/10.1016/j.bbamcr.2011.01.030

Whereas Ca2+ signalling in ventricular cardiomyocytes is well described, much less is known regarding the Ca2+ signals within atrial cells. This is surprising given that atrial cardiomyocytes make an important contribution to the refilling of ventric... Read More about Atrial cardiomyocyte calcium signalling.

Pulsating fronts in periodically modulated neural field models (2011)
Journal Article
Coombes, S., & Laing, C. (in press). Pulsating fronts in periodically modulated neural field models. Physical Review E, Article 011912. https://doi.org/10.1103/PhysRevE.83.011912

We consider a coarse grained neural field model for synaptic activity in spatially extended cortical tissue that possesses an underlying periodicity in its microstructure. The model is written as an integro-differential equation with periodic modula... Read More about Pulsating fronts in periodically modulated neural field models.

Neural fields with sigmoidal firing rates: Approximate solutions (2010)
Journal Article
Coombes, S., & Schmidt, H. (2010). Neural fields with sigmoidal firing rates: Approximate solutions. Discrete and Continuous Dynamical Systems - Series A, 28(4), 1369-1379. https://doi.org/10.3934/dcds.2010.28.1369

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of... Read More about Neural fields with sigmoidal firing rates: Approximate solutions.

Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks (2010)
Journal Article
Hlinka, J., Hlinka, J., & Coombes, S. (2010). Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks. Physical Review Letters, 104(6), https://doi.org/10.1103/PhysRevLett.104.068101

Ultraslow fluctuations (0.01-0.1 Hz) are a feature of intrinsic brain activity of as yet unclear origin. We propose a candidate mechanism based on retrograde endocannabinoid signaling in a synaptically coupled network of excitatory neurons. This is k... Read More about Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks.

Large-scale neural dynamics: Simple and complex (2010)
Journal Article
Coombes, S. (2010). Large-scale neural dynamics: Simple and complex. NeuroImage, 52(3), 731-739. https://doi.org/10.1016/j.neuroimage.2010.01.045

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models... Read More about Large-scale neural dynamics: Simple and complex.

Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map (2010)
Journal Article
Laudanski, J., Sumner, C., & Coombes, S. (2010). Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map. Physical Review E, 82(1), Article e011924. https://doi.org/10.1103/PhysRevE.82.011924

Thalamocortical (TC) neurones are known to express the low-voltage activated, inactivating Ca2+ current IT. The triggering of this current underlies the generation of low threshold Ca2+ potentials that may evoke single or bursts of action potentials.... Read More about Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map.

Understanding cardiac alternans: a piecewise linear modeling framework (2010)
Journal Article
Thul, R., & Coombes, S. (2010). Understanding cardiac alternans: a piecewise linear modeling framework. Chaos, 20, https://doi.org/10.1063/1.3518362

Cardiac alternans is a beat-to-beat alternation in action potential duration (APD) and intracellular calcium (Ca²⁺) cycling seen in cardiac myocytes under rapid pacing that is believed to be a precursor to fibrillation. The cellular mechanisms of the... Read More about Understanding cardiac alternans: a piecewise linear modeling framework.